Cross Section
Maths: Edexcel GCSE Higher, topic 4.2.6
Cross-sections of Prisms and Cylinders
Learn what a cross-section is and how to identify the uniform 2D shapes created when slicing square-based prisms, triangular prisms, and cylinders.
What is a cross section?
A cross section is the 2D shape exposed when you make a straight slice through a 3D object
Imagine taking a straight knife and cutting directly through a solid shape
The flat surface that is revealed along the cut is called the cross section
Uniform cross sections
If you slice a shape parallel to its base and get the exact same 2D shape every time, the cross section is uniform
Prisms are specific 3D shapes that have a uniform cross section along their entire length
Because of this property, a prism is always named after the 2D shape of its cross section (e.g., a triangular prism)
Horizontal slice of a cylinder
Slicing a solid cylinder horizontally, parallel to its base, creates a uniform cross section
This is the same 2D shape regardless of where you cut along the height
The horizontal cross section of a cylinder is always a circle
Vertical slice of a cylinder
A vertical cross section is created by slicing a 3D object straight down, perpendicular to its base
When you slice a cylinder vertically through its center, you are cutting through its height and its diameter
This reveals a flat, 2D surface in the shape of a rectangle
The dimensions of this rectangle are equal to the height and the diameter of the original cylinder